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HOMEWORK 2 MATH-GA 2350.001 DIFFERENTIAL GEOMETRY I (due by October, 3, 2016)
1. Show that the vector bundle constructed in 6e) of the Howework 1 is isomor- phic to the tangent bundle of RPn.
2. Let M be a compact manifold. Let p : E → M be a vector bundle. Show that one could embedE as a subbundle of a trivial vector bundle over M. 3. Let M be an n-manifold of class Ck. Show thatM is trivializable if and only
if Γk(T M) is a freeCk(M)-module of rank n.
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